Is it really the case that no statements about individual events are possible in quantum mechanics?
This statement does indeed need to be made a little more precise: if the probability of an event is 0 or 1, statements about individual events can be made as well. As an example, we can consider the double-slit experiment:
There are, in fact, places on the screen where no photons are found at all. The probability of finding a photon there is 0. Therefore, for every individual photon detected on the screen, one can predict with certainty that it will not be found at these places. In this way, a definite prediction about an individual event has been made.
Another example: if an ensemble of quantum objects has been prepared for a particular property — for example, an electron beam for the property “momentum 
” — one can predict with certainty that a momentum measurement will yield the value . The corresponding probability is 1.
However, it is immediately obvious that these special cases, in which predictions about individual events can be made with certainty, are only special cases of statistical statements with probability 0 or 1. In this respect, the statement still holds that in quantum mechanics only statistical predictions can be made.